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On projective degenerations of Veronese spaces

Edoardo Ballico (1996)

Banach Center Publications

Here we give several examples of projective degenerations of subvarieties of t . The more important case considered here is the d-ple Veronese embedding of n ; we will show how to degenerate it to the union of d n n-dimensional linear subspaces of t ; t : = ( n + d ) / ( n ! d ! ) - 1 and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to postulation...

On ramified covers of the projective plane II: Generalizing Segre’s theory

Michael Friedman, Rebecca Lehman, Maxim Leyenson, Mina Teicher (2012)

Journal of the European Mathematical Society

The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in 3 . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, B and E , we give a necessary and sufficient condition for B to be the branch curve of a surface X in N and E to be the image of the double curve of a 3 -model of X . In the classical Segre theory, a plane curve...

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